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Question 1182886: WRITE THE EQUATION OF THE LINE PARALLEL TO 4X-5Y-10=0 THAT PASSES THROUGH (0,-3).
Found 6 solutions by mananth, greenestamps, josgarithmetic, ikleyn, CPhill, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! PARALLEL
4 x + -5 y = 10
Find the slope of this line
make y the subject
-5 y = -4 x + 6
Divide by 1
y = -4 x + 6
Compare this equation with y=mx+b
slope m = -4
The slope of a line parallel to the above line will be the same
The slope of the required line will be -4
m= -4 ,point ( -2 , 2 )
Find b by plugging the values of m & the point in
y=mx+b
2 = -4.00 + b
b= 6.00
m= -4
Plug value of the slope and b in y = mx +b
The required equation is y = -4 x + 6.00
Answer by greenestamps(13295)  (Show Source):
You can put this solution on YOUR website!
The process used by the other tutor is valid; but as usual her work contains errors, leading to a wrong answer.
But her process is not very efficient; it is not necessary to find the slope of the given line to solve the problem.
Instead, use the fact that any line parallel to the given line 4x-5y-10=0 will have an equation of the form 4x-5y+C=0. Plug in the coordinates of the given point to find the value of C to complete the equation.
4(0)-5(-3)+C = 0
15+C = 0
C = -15
ANSWER: 4x-5y-15=0
Answer by josgarithmetic(39730)  (Show Source):
Answer by ikleyn(53612)  (Show Source):
You can put this solution on YOUR website! .
WRITE  AN EQUATION OF THE LINE PARALLEL TO 4X-5Y-10=0 THAT PASSES THROUGH (0,-3).
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The solution in the post by @mananth is TOTALLY and FATALLY wrong.
His errors starts from the point where @mananth incorrectly determined the slope.
I came to bring a correct solution.
Any line parallel to the line 4x - 5y - 10 = 0 has an equation
4x - 5y = c,
with the same form ax + by as the original line has, and some constant 'c' in the right side.
To find 'c', substitute coordinates of the given point into equation (1). You will get
c = 4*0 -5*(-3) = 0 + 15 = 15.
So, the sought equation is
4x - 5y = 15. ANSWER
Solved.
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Regarding this post by @mananth (and many other similar his posts), I see that this person
even does not read what he posts to the forum and does not check it.
It is simply not interesting to him, what he produces - true or false.
I know (I just deciphered it about a month ago) that @mananth is, actually, a computer code,
aka an early version of Artificial Intelligence.
It is very dangerous to trust to such a code (and to such a person) creating files/"solutions"
for teaching students, because it is not interesting to him (both to the code and to the person)
what really he creates and what really he submits to the Internet.
The only thing which is interesting to him is to occupy a space / (a territory).
Answer by CPhill(2189)  (Show Source):
You can put this solution on YOUR website! 4 x + -5 y = 10
Find the slope of this line
make y the subject
-5 y = -4 x + 6
Divide by 1
y = -4 x + 6
Compare this equation with y=mx+b
slope m = -4
The slope of a line parallel to the above line will be the same
The slope of the required line will be -4
m= -4 ,point ( -2 , 2 )
Find b by plugging the values of m & the point in
y=mx+b
2 = -4.00 + b
b= 6.00
m= -4
Plug value of the slope and b in y = mx +b
The required equation is y = -4 x + 6.00
Answer by n2(51) (Show Source):
You can put this solution on YOUR website! .
WRITE THE EQUATION OF THE LINE PARALLEL TO 4X-5Y-10=0 THAT PASSES THROUGH (0,-3).
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Yesterday (Jan.19, 2026) I witnessed strange behavior from @CPhill on this forum.
A couple of days ago I refuted an incorrect solution provided by @mananth at this spot.
@mananth's solution was incorrect due to elementary arithmetic errors that he made on the way.
OK, let's check the @CPhill (=the @mananth) answer y = -4x + 6.00.
For it, substitute the coordinates of the point (0,-3) into this equation.
Then the left side is y=-3, while the right side is -4*0+6 = 6.
So, the equation is not satisfied; hence, the point (0,-3) does not belong to the line.
Thus, the @mananth's solution had nothing in common with the correct solution -
which is why I redid/corrected/fixed it.
Now @CPhill has copied and reposted this incorrect solution by @mananth again.
This is not the only such action by @CPhill.
Yesterday, @CPhill made several (about 15) other similar actions of the same kind with other posts
where I refuted @mananth's solutions.
I consider these @CPhyll's actions to be wrong, leading to a distortion of the truth on this forum.
Therefore, I strongly protest against such actions by @CPhill and consider it necessary that visitors
to this forum be aware of this.
I recommend to a reader to ignore the post by @CPhill.
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